A review of modeling, simulation, and control technologies of altitude ground test facilities for control application

Xitong PEI, Xi WANG, Jiashuai LIU, Miyin ZHU, Zhihong DAN,Ai HE, Kqiang MIAO, Louyu ZHANG, Zhng XU

a Research Institute of Aero-Engine, Beihang University, Beijing 100191, China

b Science and Technology on Altitude Simulation Laboratory, AECC Sichuan Gas Turbine Establishment, Mianyang 621703, China

c School of Energy and Power Engineering, Beihang University, Beijing 100191, China

d Beihang Hangzhou Innovation Institute Yuhang, Hangzhou 310023, China

e Institute for Aero Engine, Tsinghua University, Beijing 100084, China

f Institute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing 100190, China

KEYWORDS

Abstract As the pivotal test equipment of aero-engines design,finalization,improvement, modification,etc.,the Altitude Ground Test Facilities(AGTF)plays an important role in the research and development of the aero-engines.With the rapid development of advanced high-performance aeroengine, the increasing demand of high-altitude simulation test is driving AGTF to improve its test ability and level of automation and intelligence.The modeling method,simulation tool,and control technology are the key factors to support the improvement of the AGTF control system.The main purpose of this paper is to provide an overview of modeling methods,simulation tools,and control technologies in AGTF control system for future research.First,it reviews the evolution of AGTF in the world, from the early formative stage to integration stage.Then, the mathematical modeling method of AGTF for control application is overviewed.Furthermore, the simulation tools used in the AGTF control system are overviewed from numerical simulation to hardware-in-loop simulation and further to semi-physical simulation.Meanwhile, the control technologies used in the AGTF control system are summarized from single-variable control to multivariable integrated control, and from classical control theory to modern control theory.Finally, recommendations for future research are outlined.Therefore,this review article provides extensive literature information for the modeling, simulation, and control design of AGTF for control application.

1.Introduction

Altitude Ground Test Facilities (AGTF) is a ground test platform that can simulate the intake and exhaust conditions of an aero-engine without influence of weather and time.1It is responsible for most of the tests (component, overall, assessment and performance tests, etc.) of aero-engine, and plays a vital role in the research and development of the engine.1,2The AGTF is composed of air pipelines, regulating valves,coolers, control systems, hydraulic servo systems, etc.Control system is one of the most important systems in AGTF.It mainly controls the inlet temperature, inlet pressure, and exhaust ambient pressure of the aero-engine by adjusting the valves in each pipeline.This can simulate the flight conditions(flight altitude and Mach number)of the engine,so as to obtain the engine’s working performance and characteristics.At present, many countries in the world have AGTF and the ability to carry out high-altitude simulation tests of aero-engines.1

FAR33, issued by the Federal Aviation Administration(FAA),as the authoritative airworthiness clause in the field of civil aviation engines in the world,systematically stipulates the requirements for all necessary tests of aero-engines on AGTF.3Moreover,the European Aviation Safety Agency(EASA)specified in the Engine Certification Specification (CS-E) that the engine must prove stable and safe operation within the entire flight envelope in the test before obtaining the airworthiness certificate.4According to the airworthiness regulations CCAR-33-R2, issued by the Civil Aviation Administration of China, the aero-engine must pass tests to prove its safe operating characteristics.5In addition, during the development of military aeroengine,it is also necessary to verify the working characteristics,performance and functions within the entire flight envelope.According to the airworthiness regulations and the requirements of the national military standard,the aerial working characteristics of aero-engines can be tested and verified on the actual aircraft and AGTF.6Flight test conducted on actual aircraft can directly verify the performance and check the state of aero-engines in the air.However, due to the space limitation of aircraft,there cannot be installed sufficient measuring devices during flight tests,which are mainly used to measure the engine parameters during operation.Meanwhile, the tested aeroengines are usually immature,which could potentially endanger the safety of the aircraft.Due to these limitations, the engine under research may not be fully verified and checked by flight test.Therefore, the altitude simulation test of aero-engine in AGTF is a common practice all over the world.

With the development of advanced aero-engines, the requirements of the altitude simulation test have been gradually improved.The previous tests of fixed flight conditions have been unable to completely evaluate the engine performance.It is necessary to achieve continuous simulation of the flight environment in AGTF such as altitude climbs at constant Mach number, accelerations and decelerations at constant altitude, and complex profiles, so that the tested engine is like‘‘flying”in the air.This puts forward high requirements for the control system to ensure the high accuracy of flight condition simulation.Since the establishment of AGTF, the United States, Germany, Canada, China, etc.have carried out a lot of research,especially in the 21st century, and the research on the control system of AGTF has entered a period of rapid development.In general, to support the research of advanced control technology, it is necessary to carry out high-precision mathematical modeling of AGTF.On the one hand, it is used for nonlinear system simulation to verify the effectiveness of control algorithms.On the other hand, it can be used for mechanism research, personnel training, fault diagnosis, etc.7Based on the mathematical model, a variety of simulations can be carried out, which can be divided into digital simulation, hardware in the loop simulation, semi-physical simulation, etc., according to different simulation tasks and purposes.For control technologies,PID control,optimal control, robust control, adaptive control and other control methods have been studied, which has improved the multivariable control ability and anti-interference ability of high-altitude flight environment simulation, and has a trend from singlevariable,steady state,slow transition state,fixed point simulation to multivariable, high response, fast target tracking,strong anti-interference, trajectory simulation and other complex control directions.

The research on modeling,simulation,and control technology of AGTF is rich, but these studies have not been systematically summarized at present.Therefore, this paper will review the development of modeling, simulation and control technologies of AGTF.This paper is organized as follows:Section 2 summarizes the historical development of AGTF,Section 3 introduces the modeling method, Section 4 introduces the model-based simulation tool, Section 5 summarizes the research on the control technology of AGTF, Section 6 gives the future development direction of AGTF control system, and Section 7 draws the conclusions.

2.Evolution of altitude ground test facilities

2.1.Introduction of altitude ground test facilities

The AGTF adopts similar principles to simulate the flight conditions of the engine when it is flying in the air.The flight conditions can be simulated by providing airflow at pressures and temperatures experienced by the engine during flight.The AGTF plays a vital role throughout the evolutionary process of aero-engines.The AGTF is generally composed of power system, air supply system, air extraction system, Flight Environment Simulation System (FESS), Data Acquisition and Processing System (DAPS), etc.One of the most important systems for the AGTF is the FESS, which consists of valves,hydraulic pump stations, electronic control system, test chamber, gas cooling system, etc.Fig.1 illustrates a typical schematic diagram of AGTF.

The power system provides power supply for compressors,valves, hydraulic pump stations, lighting, etc.The air supply system can provide the FESS with air at a specific temperature and pressure.The extraction system is mainly used for gas compression and discharge.The FESS is mainly used for regulating intake temperature, pressure and exhaust environmental pressure.The test chamber is usually divided into Intake Pressure Stabilizing Chamber (IPSC) and high-altitude chamber.The IPSC is mainly used for setting the air flow field to make it more uniform.The high-altitude chamber is used to install the tested engine and measuring device, and provide high-altitude pressure environment for the engine.The gas cooling system uses cooling water to cool the hightemperature gas discharged from the engine, so that the gas temperature meets the requirements of the extraction compressor.The DAPS is mainly used for the acquisition, processing and storage of engine test data.

Fig.1 A typical schematic diagram of AGTF.

2.2.Overview of the development of altitude ground test facilities

Since the first AGTF for ramjet engine was built in Germany in 1937, many test bases that include different types of AGTF have been built in Germany, USA, Russia, China, etc.1At present, there are dozens of test centers of AGTF in the world including hundreds of high-altitude test cells and countless component test equipment.Among them, Arnold Engineering Development Complex (AEDC), as shown in Fig.2,8is the most advanced complex of altitude ground test facilities in the word.Generally speaking, the development process of AGTF in the world mainly goes through five stages, including birth period, growth period, maturity period, completion period, and integration period.1In the view of control system of AGTF, the development process also illustrates distinct stage characteristics.In the birth period,the regulation of the temperature and pressure of AGTF is dependent on pure manual machinery regulating, without even introducing automatic control.In the growth period,the main means of regulation was the semi-automatic hydraulic system.In the maturity period, the hydraulic automatic control technology was introduced in the control system to improve the level of automation of AGTF.In the completion period, the electronic control system was adopted in AGTF and started to use closed-loop control and other means to achieve automatic control.In the integration period, the control system of AGTF has been upgraded, more advanced digital electronic control system has been used, and more advanced control methods have gradually been introduced into the control system, which promote the development of AGTF towards the direction of intelligent control.A brief summary of the technology development of AGTF is shown in Table 1.As we can see from Table 1, with the development of the aero-engine, the test equipment of AGTF has went through the periods from birth to maturity and further to integration, and the test ability of AGTF has been greatly improved.

2.2.1.Birth period

Since the late 1920s,a lot of research of high-altitude wind tunnel test and high-altitude simulation test of aircraft propulsion system has been carried out in the United States, the United Kingdom,France,etc.The research was aimed at the influence of propulsion system on full-scale aircraft and the characteristics of piston engine and jet engine.1

In 1923, the Variable Density Tunnel (VDT) of National Advisory Committee for Aeronautics (NACA) became operational at Langley field and was used to obtain high Reynolds number data on a wide range of aircraft and airship types.9The UK was impressed by the results from the VDT,and then a similar tunnel was built at the National Physical Laboratory(NPL) at Teddington a decade after the USA.9In 1938, the Hispano-suiza wind tunnel was built in France for open wind tunnel test.1,10In order to satisfy the development air cooled piston engine, the Cleveland wind tunnel was established in 1943.The tunnel has the ability to simulate temperature and pressure within certain range and the simulated altitude is up to 16 km.1In 1944,Germany placed in operation the Bavarian Motor Works engine test facilities to test and develop gas turbine engines.8

With the advent of the turbojet engine, the increasing demands for high-altitude simulation tests under larger flight conditions forced the development of improved aerodynamic test facilities.It was in this period that the AGTF and the high-altitude simulation test techniques began to develop gradually.1

Fig.2 Part of AEDC.8

2.2.2.Growth period

From 1945 to 1965, the AGTF has witnessed vigorous development.During this period, with the expansion of aeroengine flight work envelope and the frequent changes in flight operating conditions, it was no longer possible to accurately infer the high-altitude flight performance of the engine and fully reflect the application characteristics of aero-engine high-altitude flight only based on the results of component tests and ground test bed tests.1Therefore, large aeroengine high-altitude simulation test equipment in the USA,8,11–14UK,15,16the Soviet Union,17France and other countries have been vigorously developed, and especially during the period 1950–1955, the development climax was reached.1In 1950, the Soviet Central Aero-engine Research Institute began to build the Soviet Union’s only large aeropower plant test and research base in Durayev village.1By the late 1950s, the United States had built and expanded seven aero-engine altitude simulation test bases, with 16 altitude test cells;1,8Britain had established four aero-engine altitude simulation test bases, with seven altitude test cells;France had established an aero-engine altitude simulation test base with six altitude test cells.The most typical test facility was the No.3 test cell of the National Gas Turbine Establishment (NGTE), which became operational in 1958.15,16This test cell with a diameter of 6.1 m and a length of 17 m, which has test capability of simulating flight conditions at altitudes up to 24 km, at speeds up to Mach 2.3, for engines mass flow rate up to 272 kg/s and can be widely used for engine performance and function tests.1,15

In the aspect of altitude simulation test technology, in the early 1950s, the study only focused on the high-altitude steady-state performance test of aero-engine, while in the late 1950s, the study gradually shifted to the performance and function test of the transition state, such as the study of airborne starting, intake distortion and departure match.1

By the early 1960s,after a lot of practice,the United Kingdom, the United States, France and other countries have cancelled the flight test bench test stage in the development of aero-engine propulsion system, and a large number of engine altitude test tasks transferred to AGTF.1,8,11–16During this period, the new construction and expansion of AGTF have been further increased all over the world.The United States built 16 new altitude test cells; Britain built two altitude test cells; France built a new altitude test cell; Canada built an aero-engine altitude simulation test base;18Germany built a new small AGTF for teaching.19–22

To solve the compatibility of the inlet and the engine in the supersonic vehicle, there are two different technical ways for the high-altitude simulation test of the propulsion system.The first is the free jet simulation test, and the second is the propulsive wind tunnel test that can simulate the flow inside and outside the inlet.The former is more economical, and the latter is costly.Britain,France,the Soviet Union and other countries chose the first technical way and built free jet high altitude test cell in the 1960s1.Only the United States chose the second technical way and built the world’s first propulsion wind tunnels,16 T and 16S,at the Arnold Engineering Development Center in 1956.These two wind tunnels have the ability to conduct full-scale intakes/engines/nozzles combined testing.23–25

2.2.3.Maturity period

From 1965 to 1980,whether from the scale and integrity of test facility, or from the level of test technology and theory, the AGTF in the world gradually became mature.During this period, with the rapid development of aero-engine, the aviation powers in the world all increased the construction and investment of AGTF, which further promoted the development of AGTF.1

In 1973, the Propulsion Systems Laboratory (PSL) at NASA Glenn Research Center (GRC) constructed two altitude simulation test chambers, PSL-3 and PSL-4, which were commissioned for turbine engine research studies.26–29These two test chambers are each 7.3 m in diameter and 11.9 m long.They are directly connected facilities in which the engine is connected through inlet ducts to the inlet plenum.Each chamber utilizes the NASA GRC central air services for supply of pressurized air to set the inlet conditions and altitude exhaust for altitude simulation.The functional layout of PSL is illustrated in Fig.3.26PSL is NASA’s only ground-based, fullscale engine test capability designed for research to provide detailed information on the performance and operability of engines and propulsion systems under extreme conditions over the entire flight envelope,which can only be obtained through altitude-simulated ground-based testing.The overall facility capabilities of PSL are shown in Table 2.26–29

During this period,the Soviet Union expanded the test base in Durayev village.They not only built a large air source station and many component test facilities,but also constructed a new altitude test chamber for free-jet test.After the expansion and upgrade, the test capabilities of the test base have greatly improved: the maximum mass flow of air supply system was increased to 650 kg/s; the simulated altitude was improved to 22 km; the simulated flight speed was up to Mach 3.1

With the continuous development of high-altitude simulation test technology,advanced test equipment and test technology were constantly applied to AGTF, and the high-altitude simulation test capability was constantly improved.During this period, many powerful and advanced AGTFs began to be built.In the decades that followed, these test platforms played an important role in the development of advanced aero-engines.

2.2.4.Completion period

From 1980 to 1995, due to the development of high bypass ratio turbofan engines and the further improvement of combat technical indicators of fighter aircraft, the existing highaltitude simulation capability could not meet the requirements of high-altitude test of engines, which promoted the development of AGTF towards the direction of complete function.8,11

In 1985, the Aeropropulsion Systems Test Facility (ASTF)at AEDC was constructed for testing integrated, full-scale propulsion systems under simulated flight conditions more representative of modern airbreathing turbine engines.8Located on a 57-acre site,ASTF is an open-circuit facility with two tests cells, C-1 and C-2, each with an 8.5 m diameter and 25.9 m long.11The aerial view of ASTF is illustrated in Fig.411.ASTF provides the United States with the unique test capability of simulating flight conditions at altitudes up to 30.5 km, at speeds up to Mach 3.8, and inlet mass flow rate up to 680.4 kg/s.The test and control system of ASTF is powerful and complete.The control of the whole system is fully automated and the state of inlet and exhaust can be set directly by the computer.The test systems in the two chambers are capable of recording steady-state and transient data for up to 3500 parameters and can be operated remotely in parallel.The measurement of air flow is carried out with a plurality of venturi tubes, and the measurement of fuel flow is carried out with a multi-range fuel measurement system to ensure the accurate measurement of air flow and fuel flow throughout the working range of the engine.As one test cell of ASTF, C-1 is mainly used for military engine tests.It is the main test cell for AEDC to test high-flow military engines,and it is also one of the most advanced high-altitude chambers in the United States.Many engines have been tested in C-1, such as the Pratt & Whitney F119 engine (Fig.511) used to power the Lockheed F-22A Raptor, the General Electric F414 engine used to power the Boeing Super Hornet F/A-18E/F and the Pratt & Whitney F135, and General Electric F136 engines used to power the Joint Strike Fighter (JSF), the Lockheed F-35 Lightening II.C-2 is mainly used for civil engine tests, including the PW4000 series engines, Rolls-Royce Trent 900, Alliance GP7200 (Fig.611), etc.In general, whether from the scale and integrity of test facility, or from the level of test technology, the AGTF in this period was fully functional.8,11,12

2.2.5.Integration period

Since the mid of 1990s, the cost and risk of high-altitude simulation tests have been increasing with the continuous improvement of aircraft technical indicators and the emergence of new concept engines and aircraft on the other hand.Therefore, the high-altitude simulation test base of a country presents the development trend of resource and advantage integration.At the same time, the research of intelligent high-altitude simulation test technology has also been carried out and applied.For example,the United States basically integrates its aero-engine high-altitude simulation resources through AEDC.1,8,11

With the collapse of the Soviet Union and the end of the Cold War, the world pattern changed dramatically and the field of aviation technology was also affected.1European and American countries, especially the United States, began to re-examine the development layout and future planning of the aviation industry.In the early 1990s, the United States reformed its domestic military R&D system, emphasizing resource integration and functional division.During this period,a large number of the original AGTF in the United States were integrated.Many research and development institutions were canceled, and a large number of technologies and equipment were incorporated into AEDC.After this big institutional change, the high-altitude simulation facilities in AEDC have also gained considerable development.At present,AEDC is the most advanced and largest complex of flight simulation test facilities in the world.AEDC operates 43 turbine and rocket engine test cells, space environmental chambers, aerodynamic and propulsion wind tunnels, arc heaters, ballistic ranges and other specialized units.1,11

Fig.3 Functional layout of PSL.26

Table 2 Overall facility capabilities of PSL.26–29

Fig.4 Aerial view of ASTF.11

Fig.5 Pratt & Whitney F119 in ASTF test cell C-1.11

Fig.6 Engine Alliance GP7200 in ASTF test cell C-2.11

3.Overview of mathematical modeling of AGTF for control application

The mathematical model of AGTF is mainly used for controller design and simulation verification.The modeling process of AGTF for control application usually includes two steps.The first step is to establish the AGTF’s component models based on mechanism modeling methods, and the second step is to build the system-level nonlinear simulation platform by using the component models.The AGTF components include pipelines, regulate valves, compressors, heat exchangers, exhaust diffuser, etc.This section will give an overview of the current modeling methods for each component.

3.1.Pipeline modeling

As for AGTF, the desire is always to simulate the conditions(inlet total temperature and total pressure, altitude pressure)as close to the conditions that the engine will encounter during flight as possible.2Therefore, the most important thing of mathematical modeling is to capture the dynamic process of the air or gas in the AGTF for the simulation system and control system design of AGTF.The dynamic process is mainly characterized by the flow of air in the pipeline, so the key to modeling is to establish a suitable pipeline model.For the convenience of explanation, we call the process of describing the state change of the fluid in the pipeline as pipeline modeling.At present,there are three methods:lumped-parameter control volume method, quasi-one-dimensional finite volume method and multi-cavity iterative modeling method.

3.1.1.Lumped-parameter control volume method

The lumped-parameter control volume method is a simple and effective way to model the temperature and pressure differential equation of various tanks and other large volumes in AGTF despite being of low-fidelity.30However, because the lumped-parameter control volume does not account for spatial effects, any loss such as bends, friction, or sudden changes in area is not incorporated directly into the calculations,and this method does require considerable tunings to improve the accuracy of the established model.To tune a lumped-parameter model, there must be sufficient facility data available to adequately describe loss coefficients and efficiencies.31Another shortcoming to lumped-parameter control volume modeling is the assumption that all flow properties are uniform within a defined boundary.This method also indirectly assumes that all the associated mixing processes are taken place instantaneously.31Although the lumped-parameter method has these shortcomings, it also has advantages in engineering application.The lumped-parameter method is easy for modeling and engineering implementation and is suitable for large facility modeling and real-time simulation due to the advantage of saving computational resources.30–32

Borairi and Van Every investigated the dynamic process modeling of the inlet air treatment system of the highaltitude test facility in Ottawa, Canada with the lumpedparameter control volume method.33For the abstract schematic diagram of a pipe control volume illustrated in Fig.7,they give the temperature and pressure differential equation of the control volume deduced by constant specific heat.According to Ref.33,the temperature and pressure differential equation of the control volume are given as follows:

where Tiis the air temperature at location i; Piis the air pressure at location i;m˙iis the air mass flow rate at location i;V1_2is the volume of the pipe control volume;R is the gas constant;Cvis the specific heat at constant volume; ˙Q1_2is the heat transfer rate between the pipe control volume and surroundings; γ is the specific heat ratio.

Zhu et al.deduced the temperature and pressure differential equation of control volume in a general way by variable specific heat.2,34The schematic diagram of generalized control volume is illustrated in Fig.8.34Applying the ideal gas state equation and conservation of mass and energy, the general form of temperature and pressure differential equation of the control volume are obtained as follows:

where T,P,and h are temperature,pressure,and enthalpy of the control volume respectively;Tini,Pini,m˙ini,Cini,and hiniare temperature, pressure, mass flow rate, average flow velocity, and enthalpy of the i-th inlet of the control volume respectively;m˙outjand Coutjare mass flow rate and average flow velocity of the j-th outlet of the control volume respectively; cPis specific heat at constant pressure; V is the volume of the control volume; ˙Q is heat transfer rate between the control volume and surroundings.

For the heat transfer process of control volume, Zhu et al.considered it as the process of a long tube with insulation boundary condition.2,34,35Consider a long tube with inner radius of r0,thickness of D,length of L,density of ρ,conductivity of kt,and specific heat of ct.The direction of the conduction that is along the radial direction is considered.36The long tube is divided into N+1 thin tube by using nodes 0,1,2,???,j–1,j,j+1,???,N–1,N, which is illustrated in Fig.9.35The derivation of the heat transfer of the long tube can be found in Ref.2.hfis the average convection heat transfer coefficient.Tmis the average temperature of the fluid.The temperature differential equations of the N thin tube are obtained as follows:

Fig.7 Schematic diagram of a pipe control volume.33

Fig.8 Schematic diagram of generalized control volume.34

Then,according to Newton’s law of cooling,the heat transfer rate between control volume and surroundings is obtained as2

where ˙Qpis heat transfer rate between the control volume and surroundings.

The lumped-parameter control volume method was applied to establish the math model of the Aerodynamic and Propulsion Test Unit(APTU),located at AEDC.30The comparisons of simulated stilling chamber total temperature and pressure predictions and facility data for a typical run are illustrated in Fig.10.30It can be seen from Fig.10 that the lumpedparameter control volume based model works sufficiently well to capture the dynamic of the stilling chamber.Sabine used the lumped-parameter control volume method to set up the math model of Stuttgart AGTF also with promising results as shown in Fig.11.21

Sheeley et al.30,32relayed experiences and ‘lessons learned’from constructing and using control volume of wind tunnels and AGTF, including hardware-in-the-loop configurations.They found that the control volume method can cause problems such as oscillations in pipes and between volumes with large area interfaces.To address the oscillation problem in control volume based model, Sheeley investigated the use of fuzzy logic control techniques to modify the mass flow rate between two control volumes based model to increase stablilty in smulation.32A simple system,consisting of two tanks separated by a control valve,was chosen as a test case(see Fig.12)to verify the effectiveness of the fuzzy logic modifier.32The aim behind the design of the modifier was to adjust the mass flow rate only when unstable or oscillatory behavior was evident.The basic architecture of the fuzzy logic modifier is illustrated in Fig.13.32Due to the fact that the rapid change in the pressure difference between volumes is the source of unstable behavior,the mechanism of the modifier is to reduce the magnitude of the mass flow rate when the time rate of change in the pressure difference between volumes is large relative to its nominal value to prevent the unstable behavior.The details of the fuzzy logic modifier can be found in Ref.32.The comparison result of unmodified system with fine time step and modified system with a large time step is illustrated in Fig.14.32It can be seen from Fig.14 that although with a large time step,the modified system is well behaved and reaches the steady-state condition at almost exactly the same time as the unmodified ‘‘true” solution.The fuzzy logic modifier provides a way to increase stability and impoves simulation speed of control volume based facility model, which enhances the advantage of control volume method in large facility modeling and real-time simulation.

3.1.2.Quasi-one-dimensional finite volume method

Fig.9 Heat transfer model schematic diagram of long tube.35

Fig.10 Comparison between simulation results and facility data.30

Fig.11 Comparison between simulation results and measured data (the figure text is in German).21

To alleviate some of the shortcomings of the lumpedparameter method mentioned above, a Quasi-one-Dimensional Finite Volume Method (QDFVM) using central differencing on a staggered grid was presented by Brett.31Since the conservation of mass, momentum, and energy are considered in the deduction of the QDFVM,losses can be included in the calculations with the addition of a momentum equation.Therefore, the effects of friction, area change, and the minor losses (such as those resulting from bends in the pipe system)are accounted for directly in the new volume method.Furthermore, heat transfer is calculated at a local level rather than being lumped globally as in the lumped-parameter control volume method.Fig.15 illustrates the new capabilities of the QDFVM compared with the lumped-parameter method.31

Fig.12 Two tanks system as test case.32

Fig.13 Schematic of fuzzy logic modifier.32

In the QDFVM, the staggered grid approach is the key to consider momentum equation.The staggered grid is illustrated in Fig.16.31The momentum equation is calculated at the cell faces.The mass and energy equations are calculated at the cell centers.

For the I-th cell, the equation for calculating the time rate of change of mass is given as follows:

For the i-th cell face, the equation for calculating the time rate of change of mass flow is shown as follows:

Fig.14 Comparison of unmodified system with fine time step and modified system with a large time step.32

where v is the velocity of the fluid,f is the friction factor,A is the surface area, DHis the hydraulic diameter, K is the loss coefficient, and Δx is the distance between adjacent cell centers.The calculation of these parameters can be found in Ref.31.

For the I-th cell,the time rate of change of energy is calculated as.

Fig.16 Staggered grid.31

where E is the energy of the fluid of the control volume; QIis the heat transfer of the I-th control volume.

Brett verified the ability of the QDFVM to accurately calculate equilibrium results of the ducting problems with changes in duct cross sectional area, minor momentum losses,friction,and localized heat transfer effects by the example pipe demonstrated in Fig.17.31The simulation results of the QDFVM model were consistent with the known analytical solutions to isentropic, Rayleigh, and Fanno flow problems under proper grid size and flow Mach number.Example comparisons of the QDFVM model with analytical solution of isentropic flow are presented in Fig.18.31He also investigated the influence of grid size on the simulation error in the QDFVM model.Fig.1931shows the static temperature and pressure percent error of the QDFVM model with different grid sizes.It is found that with the increase of the grid spacing,the accuracy of the QDFVM model reduces.He also found that the steady-state numerical results of the QDFVM model appeared to be deviating further from theory solutions as flow Mach number was increased.Therefore,the grid size and flow Mach number should be carefully focused when using the QDFVM for modeling.

A representative piping network in an AGTF was used by Brett to compare the QDFVM with lumped-parameter volume method.It was found that the QDFVM proved more accurate for simulating transient response of the piping network system.The lumped-parameter model overpredicted the steady-state total pressure of the ‘‘warm leg” by 8% and mass flow rate by more than 50%.This is directly due to the uniform pressure that is calculated by the lumped-parameter method.When pressure is allowed to vary naturally along the length of the duct as in the QDFVM model, more accurate mass flow predictions are obtained.As a result, the control valves upstream and downstream of the piping network experience a smaller pressure difference, unlike that computed by the lumpedparameter method.

Fig.17 Geometry of example pipe.31

Fig.18 Static temperature and pressure comparison with isentropic flow theory for compressible flow.31

Fig.19 Static temperature and pressure percent error for varying grid sizes.31

Rennie used a similar method to divide the wind tunnel into several small sections of pipes, as shown in Fig.20.37Under the assumption of one-dimensional and constant fluid properties, based on the conservation of mass, energy and momentum, Rennie established a mathematical model of the wind tunnel, which can reflect its transient thermal behavior.36–38Different from Boylston’s completely mechanism-based modeling, Rennie carried out a lot of tests to determine the total pressure loss coefficient,forced convection and natural convection heat transfer coefficient required in the model,so that the wind tunnel model is basically consistent with the actual characteristics.On this basis, Rennie further studied the wind tunnel model under the wind tunnel main fan acceleration,periodic louver oscillations and other scenarios.This verified the validity of the model for predicting the airflow characteristics in the wind tunnel, and Rennie suggested that the model would be integrated into the wind tunnel feedforward control system to improve the performance of the closed-loop control system.38

Fig.20 Structural diagram of Notre Dame 3 Foot Wind Tunnel.37

The above research gives the theory of quasi-onedimensional flow modeling.However, AGTF is a large-scale testing equipment integrating pipes, regulating valves, mixers,air sources and other components.It is necessary to take advantage of the quasi-one-dimensional flow and apply its modeling method to other components to improve the dynamic accuracy of component level and system level models.Based on the quasi-one-dimensional flow method, Pei et al.established various component models of AGTF (such as pipes, regulating valves, mixers, multi-inlet and multi-outlet chambers, etc.), and built a system level numerical simulation model, as shown in Fig.21.39In particular, the quasi-onedimensional flow chamber is transplanted to AGTF regulating valve, and combined with the steady-state flow characteristic model of regulating valves in Section 3.2.1 to form a model that can reflect the dynamic and heat transfer characteristics of regulating valve.The simulation results of the system level model further prove that it can support the development and verification of the controller.On this basis, Liu et al.further extended the quasi-one-dimensional flow method to all components of AGTF, and proposed the concepts of central control volume,boundary control volume and virtual control volume.Then, a generic modeling method of quasi-one-dimensional flow for AGTF is systematically presented, which makes system level model also composed of staggered grids, as shown in Fig.22.40This can further take advantage of quasi-onedimensional flow in considering friction, heat transfer, local loss and other factors, and reflect the spatial effect and time delay characteristics of airflow in AGTF.In addition, the interfaces of all component models are unified,which improves the universality of component models and the efficiency of system level modeling.

3.1.3.Multi-cavity iteration modeling method

The multi-cavity iteration method is mainly used for modeling irregular pipeline flow processes,such as the exhaust system of AGTF.The exhaust system is one of the key systems of AGTF,which is composed with test chamber,exhaust diffuser,cooler,regulate valve(e.g.,butterfly valve)and pipe volume shown in Fig.2341.The components could be modeled separately,organized with the structure in Fig.23, and solved with iteration method.The most difficult problem in modeling is ejection calculation and representation of nonlinearity along the gas path,which is solved with the multi-cavity iterative modeling method presented in Ref.41.It overcomes the disadvantage that traditional lumped parameters model cannot calculate the ejection factor and dynamic parameters along the gas path.

Calculation logic of exhaust system multi-cavity iteration model is shown in Fig.24.The states of exhaust system depend on the temperature and pressure in the test chamber and before the butterfly valve 3 which change when the flow balance of exhaust system breaks.Static pressure in test chamber(p1s) is calculated with the total mass flow passing through valve 1 and valve 2 and secondary mass flow which is ejected by the gas discharged from engine nozzle.Static pressure before valve 3 (p5) depends on the mass of mixed gas flowing out of exhaust diffuser as well as the mass passing through valve 3.Therefore, it could be concluded that dynamic states are decided by the flow of valves and nonlinear parameters of exhaust diffuser.Modeling process of different parts of exhaust system like exhaust diffuser, heat exchanger, and regulate valves will be discussed in the following sections.By organizing the components with Fig.24 and solving the equations of conservation of mass, conservation of energy, conservation of momentum and ideal gas state,nonlinear parameters could be obtained.Meanwhile,simulation results will be more accurate than lumped parameter method due to introducing multi-cavity method.Moreover,simulation speed will be much faster than quasi-one-dimensional finite volume model because of introducing iteration method for it calculates all parameters at the same time and has better convergence.

In order to simulate model with iteration method,a series of initial guess values which are necessary and unknown at the start period of calculation process must be defined.Meanwhile,the same number of residual equations must be given to obtain the real value of initial guess parameters.The iteration method could be Newton-Raphson.Taking the exhaust system illustrated in Fig.23 as an example,four initial guess values of ejection factor u,static pressure ps2at cross section 2,total pressure pt3at cross section 3 and velocity coefficient λ4at cross section 4 and four residual equations are defined with static pressure balance at cross section 2,impulse balance between cross sections 2 and 3, mass balance between cross section 3 and 4, and total pressure balance between cross sections 3 and 4.

The summary of lumped-parameter control volume method, quasi-one-dimensional finite volume method and multi-cavity iteration modeling method is illustrated in Table 3.31

3.2.Regulation valve

3.2.1.Modeling of regulation valve flow characteristics

Regulation valve is one of the most important components in AGTF.There are several types of regulation valve usually used in AGTF, such as butterfly valve,42special valve,43–46and sleeve valve47that are presented in Fig.2548.For the mathematical modeling of the regulate valve, it is necessary to build a flow model which can reflect the flow characteristics of the actual regulation valve.In engineering, the mass flow rate of regulation valve is calculated as follows:

where φ is the flow characteristic coefficient of regulation valve, which is a function of regulation valve opening VPand pressure ratio Pr=Pd/Puof regulation valve downstream and upstream pressure; S is the flow area of regulation valve,which is a function of VP; ρuis the density of valve upstream fluid; Puis the regulation valve upstream pressure; Pdis the regulation valve downstream pressure.

Fig.24 Logic diagram of exhaust system iterative model.41

Pei et al.presented an iterative method of empirical formula to obtain the flow characteristics of the special valve.44Zhu et al.studied the method to identify the flow characteristics of a large butterfly valve from limited test data.42The flow characteristics diagrams of various valves are illustrated in Fig.26.42,48Miao et al.investigated the correction method for the flow characteristics map of the special valve with neural network.46Fig.27 illustrates the comparison result of mass flow rate calculated by the corrected and original flow characteristics with test data.46After correcting, the accuracy of the flow model of the special valve greatly improved.Due to the fact that the regulation valves used in AGTF are nonstandard part, sufficient facility data are needed to correct the flow characteristics to obtain high-precision model.

3.2.2.Modeling of regulation valve dynamic characteristics

For the modeling of regulate valve dynamic characteristics,the current modeling method mainly uses the dynamics of the actuator to approximate its dynamics.The actuators of regulation valves in AGTF include pneumatic,electric and hydraulic servo drives,among which hydraulic servo drives are the mostcommon.The hydraulic servo system is mainly composed of valve-controlled hydraulic cylinders, electro-hydraulic servo valves, closed-loop controllers, sensors, etc.For the modeling of dynamic characteristics of hydraulic servo system, many scholars have conducted a lot of research.2,34,35,49,50,51Pei et al.systematically modeled the hydraulic servo system of regulation valve in AGTF, obtained the transfer function model,and established a complete hydraulic control loop model.48In order to analyze the influence of the change of aerodynamic load on the hydraulic servo system in AGTF, Jiang et al.proposed a modeling method for the electro-hydraulic servo actuator under the load change, and the established AMESim model can well describe the dynamics of the real hydraulic servo system.52Usually, the hydraulic servo system model based on a mature simulation software like AMESim has high fidelity to meet the demand for modeling the dynamic characteristics of the control valve in AGTF.

Table 3 Summary of lumped-parameter control volume method and quasi-one-dimensional finite volume method.

Fig.25 Different types of regulation valve usually used in AGTF.48

3.3.Compressor

Compressor is an important component in AGTF, which is usually used in air supply system and air extraction system to provide the desired pressure conditions.The establishment of compressor model is a process of describing guide blade adjustment of axial flow compressor by mathematical method.Because the influence of pressure on the compressor is greater than that of the gas power effect,the pressure influence is classified as the steady-state component.Because of the finite heat capacity of the structural material of the compressor,the influence of heat transfer on temperature dynamics cannot be ignored.Sabine provided a modeling scheme that combines a steady-state model and a dynamic model to establish the mathematical model of a compressor.21The modeling scheme and the module data flow with adjacent components are illustrated in Fig.2821.For the steady-state model,the mass flow rate and steady-state exit temperature are calculated based on the manufacturer’s performance map of the compressor.

Fig.26 Flow characteristic diagrams of various valves.42,48

For the dynamic model, it can be established by using the lumped parameter method or quasi-one-dimensional flow method, in which the heat transfer is considered.

3.4.Heat exchanger

Heat exchangers are devices that facilitate the exchange of heat between two fluids that are at different temperatures while keeping them from mixing with each other.They are widely used in engineering, from fluid control facilities like AGTF,to chemical processing and power production in large plants.Heat transfer in a heat exchanger usually involves convection in each fluid and conduction through the wall separating the two fluids.There are several types of heat exchanger applied in industrial area, such as double-pipe heat exchanger, compact heat exchanger,etc.The gas cooler of the AGTF is a typical heat exchanger.The corresponding model should predict the pressure drop and temperature decrease of the fluid through the gas cooler.

In the exhaust system of the AGTF, the heat exchanger shown in Fig.2941brings the heat out of the system by the cooling water to decrease the temperature of gas which will slow the process of equipment aging.Meanwhile, the gas flow capacity of the exhaust system can be improved by reducing the gas temperature.A multi-cavity model method of heat exchanger is proposed in Ref.41 which divides the equipment into a series of volumes.It calculates the nonlinear process of temperature drop.Fig.3041shows the heat transfer process.

Meanwhile, the pressure drop could be calculated by49

where Δphis the pressure drop due to the heat exchanger.Constant c depends on the Reynolds number of the gas and the structure of the heat exchanger.ρhand uhare the density and velocity of the airflow at the heat exchanger inlet respectively.

3.5.Exhaust diffuser

Fig.27 Comparison result of mass flow rate calculated by corrected and original flow characteristics with test data.46

Fig.28 Modeling scheme and module data flow with adjacent components (the figure text is in German).21

Fig.29 Structure of heat exchanger.41

Fig.30 Schematic diagram of cooling pipe heat transfer.41

The main function of an exhaust diffuser is to increase the static pressure,and reduce the temperature and velocity of the gas to release the burden of the air extraction system.In the exhaust system of AGTF, gas discharged from the engine will be mixed with air ejected from the test chamber.The gas mixing in the exhaust diffuser together with the heat exchanging and friction makes the modeling process hard.In Ref.41, a multi-cavity modeling method for the exhaust diffuser is presented.The method can be used to calculate the ejection,mixture and expansion processes with three cavities shown in Fig.31.

In the first cavity which is defined as an ejection model,the main stream will expand while the secondary flow will accelerate until the static pressure of main stream and secondary flow equals each other.Mass flow and total parameters in cross section 2 are the same as those in cross section 1.One of the most important functions of the ejection model is calculating the flow area of main stream and secondary flow.It is assumed that static pressure at cross section 2 has been obtained at the beginning and could be updated by iteration.Then,the calculation process is shown in Fig.3241.In Fig.32, subscript m means main stream and subscript s means secondary flow.

In the second cavity which is defined as mixture model,main stream and secondary flow mix with each other until even.Mass flow could be calculated with the conservation of mass.Meanwhile,temperature is calculated with the conservation of energy, and pressure could be calculated with the conservation of momentum.

In the third cavity which is defined as expansion model,the gas expands following the flow conservation law without considering heat exchange and friction.Therefore, the total temperature and total pressure at cross section 4 are the same as those at cross section 3.Then, the velocity coefficient at cross section 4 is obtained with flow formula, and static parameters could be calculated with total parameters.

3.6.Brief summary

Modeling is the basis of the subsequent simulation analysis and control design.This section summarizes the technical details of current AGTF modeling for control application.The component-level model of AGTF determines the accuracy of the final system-level nonlinear numerical simulation platform.Generally, the flow characteristics of AGTF pipelines described based on the quasi-one-dimensional finite volume method and the multi-cavity iterative modeling method are sufficient for control design and simulation verification, while the additional correction of the models of regulating valves,compressors, exhaust and expansion components can make the stability and dynamic characteristics of the system-level model have higher accuracy.

4.Overview of simulation tools in AGTF control system

The mathematical model of AGTF contains its operation mechanism.The digital simulation can more intuitively reproduce the complex physical process, providing a more convenient and rigorous test environment for the control system.In addition, digital simulation reflects the key operating characteristics of the control system of AGTF.It can be used for personnel training,software debugging and development,fault detection and diagnosis, system health assessment, etc.According to the application scenario and function, it is divided into the numerical simulation, hardware in the loop simulation and semi-physical simulation.

Fig.31 Multi-cavity exhaust diffuser model.41

Fig.32 Calculation process of static pressure balance at cross section 2.41

4.1.Numerical simulation

Numerical simulation is the most basic simulation method,which reproduces mathematical models through logic codes and programs.In the 1990s, Pratt&Whitney established AGTF numerical simulation system on the basis of accumulated test data to support the research of its control algorithm.53As the requirements for modeling efficiency become higher, Montgomery et al.developed a general model library based on the equipment characteristics for the J1 and J2 turbine engine test facilities of AEDC,and built a numerical simulation system.54Based on the modular modeling method of MATLAB/Simulink,researchers can quickly apply the general modeling method to other AGTF,and put more effort into the research of model mechanism.55Therefore,the numerical simulation system of AGTF can be further improved to more accurately reflect the physical phenomena.On the one hand,the mechanism of the existing models can be further studied to make the equipment characteristics more accurate.For example, a large number of tests or CFD simulations can be carried out to obtain more data, and more real equipment characteristics can be reflected based on artificial neural networks and fuzzy data tables.56On the other hand, it has become a major trend to build an integrated simulation system including AGTF,tested engine,control system,etc.AEDC has developed a numerical simulation platform which integrates aircraft simulator, distortion simulator, engine model, AGTF model,and control system.The platform can reflect the system characteristics of some unconventional tests.57The Stuttgart University has also established a joint closed-loop simulation system including the master controller, AGTF model, AGTF controller, aero-engine and its controller.Based on MATLAB/Simulink software, the platform has verified the influence of AGTF control system performance on aeroengine system performance test.58The numerical simulation system is important in the initial stage of the development and verification of the control system.The nonlinear characteristics of AGTF simulated by the numerical simulation system provide a verification environment for the control algorithm, which has become an indispensable verification means for the development of new control technologies.

4.2.Hardware-in-the-loop simulation

The difference between hardware-in-the-loop simulation and numerical simulation lies in the real-time requirements and hardware testing requirements.Although AGTF is still replaced by mathematical model, being real-time demands higher requirements for the design and implementation of control algorithms.Hardware-in-the-loop simulation system usually includes real-time simulator, data transmission interface,Programmable Logic Controller (PLC), simulation interface,operator interface and other hardware.PLC is required to be the real hardware equipment used by AGTF, and the rest is simulated by the real-time simulator.Fig.33 is a typical simulation hardware configuration.59

To complete the upgrade of the propulsion wind tunnel control system, AEDC designed a hardware-in-the-loop realtime simulation system.It was used to verify the control scheme, test the control algorithm, and train the operators.60In 2004, AEDC developed a hardware-in-the-loop simulation platform based on the equipment model,which has significant benefits for the development of test equipment.However, its model and simulation system still have limitations, such as incomplete model information and low model accuracy.56In 2013, Weisser et al.built a hardware-in-the-loop simulation system for AGTF of Stuttgart University, including AGTF model, AGTF control system, engine and its control system,which effectively supports the research and application of control algorithm.61

4.3.Semi-physical simulation system

The semi-physical simulation is an important and critical step before the designed controller is put into operation in the actual AGTF.Unlike the hardware-in-the-loop simulation system, the semi-physical simulation system includes the real actuators and sensors of AGTF.The nonlinear characteristics of the pipeline system are still represented by the model.

Fig.33 Typical simulation hardware configuration.59

In 2010, Zhang et al.carried out the research on the semiphysical simulation technology of AGTF based on the GE90-70 programmable control system.62In 2019, Qian et al.improved the semi-physical simulation system for air intake and exhaust control, as shown in Fig.3463.Meanwhile, a systematic design method combining simulation model and physical components is proposed.The simulation model is established by theoretical modeling and system identification methods, and the system design and software development are completed based on PLC.63

4.4.Brief summary

Each of the three simulation methods has its own advantages,and different simulation methods are suitable for different applications.Numerical simulation is simpler and more efficient, which is a simplification of the real physical process.Compared with numerical simulation, the hardware-in-theloop simulation is closer to the real physical scene by introducing hardware devices such as controllers.Compared with the hardware-in-the-loop simulation, the semi-physical simulation is the closest to the real physical scene, and the simulation is more realistic, but it requires more hardware resources.The summary of various simulation methods is shown in Table 4.

Fig.34 Semi-physical simulation system for intake and exhaust control system.63

5.Overview of control technologies in AGTF control system

Control has been the most important component since the birth of AGTF.The control system acts like a ‘brain’, which regulates AGTF to ensure the simulation of flight condition of the test engine, and determines the test ability of AGTF.With the development and application of control theory, the control technologies used in AGTF control system have gone through from single-variable control to multivariable integrated control,from classical control theory to modern control theory,and from analog controller to digital controller.There are two types of control problems in AGTF:first,the pressure control problem in inlet pressure control system or engine test chamber, which is a single-variable control problem; second,the temperature and pressure synchronous control of Flight Environment Simulation System(FESS),which is a multivariable control problem.Thus, the following will focus on the overview of the control technologies applied to address these two problems.

5.1.Single-variable control

Pressure is a typical controllable variable,which directly influences the simulated fight environment of AGTF.The Proportional-Integral (PI) controller, which is the foundation of the conventional single-variable control approach,regulates the target parameter by closed-loop negative feedback.The straightforward PI controller can only complete the test tasks with laxer performance index constraints.Under the influence of large disturbances and strong nonlinearity, linear PID cannot guarantee the control performance of AGTF.64Researchers have steadily created more derivative control algorithms based on PI control algorithms, such as feedforward PI control,61,65gain scheduling PI control,66fuzzy PI control,67etc.with the advancement of test conditions and control algorithms.

Ref.65 provides a PI control technique for adaptive realtime tuning using real-time engine characteristics as a reference.In the study, various engine operating circumstancesare fed into a tuning algorithm built on the Ziegler-Nichols technique as reference variables.This tuning process then generates effective PI controller settings for the control system in various engine operating situations.Zhu et al.applied the PI gain scheduling technique to an AGTF control system.66Their study combines the engineering viability of PI controllers with the benefits of the gain scheduling approach for solving large work envelope control challenges.Specifically, a PI gain scheduling control method for the inlet system pressure was proposed based on the structural characteristics of the inlet system, fluid properties, and control system hardware characteristics,and was compared and validated with a conventional PI controller.The control system with the addition of PI gain scheduling has a large performance increase in the control of pressure in the capacitor cavity, and the steady-state error is no more than 0.1% in the simulation tests, according to the semi-physical simulation tests.

Weisser et al.61presented a feedforward module for the control system of intake pressure.This approach uses a model-based controller dependent on measured facility parameters to calculate the positions of the inlet valves and a separate PI controller to adjust the altitude pressure pH.The schematic diagram of this feedforward control system is shown in Fig.35.61

Zhang et al.studied the pressure control system with online self-tuning of fuzzy PI parameters simulating artificial intelligence in order to lessen the necessity for model correctness.They tested it in both a real test facility and a semi-physical simulation system.67The test results demonstrated the flexibility with which the fuzzy PI control system may self-tune the control parameters live in response to indications of pressure deviation and deviation change rate.The results of the actual tests show that the ambient pressure fuzzy control system has good dynamic performance and control accuracy and complies with the system design requirements.The semiphysical simulation test shows that the system has robust performance throughout the entire working envelope range, and the initial optimal system parameters are discovered.

Fig.35 Control block diagram of feedforward control system.61

In recent years, the control approach based on Active Disturbance Rejection Controller (ADRC) has also been implemented in the control system associated to AGTF in addition to the PI control based control algorithm.ADRC is an Extended State Observer (ESO) based control technique proposed by Han.68The fundamental concept is that the total disturbance to the system includes both the unmodeled dynamic information of the system and the unknown disturbance effects.The total disturbance is calculated and the corresponding control quantity is formed by the expansion state observer.The disturbance is then removed before the disturbance affects the controlled quantity, resulting in a modelindependent active anti-disturbance technique.68In this context,Dan et al.designed an active disturbance rejection control method based on the Expansion State Observer (ESO) for the inlet environment simulation of AGTF in response to the urgent demand for strong robustness of the control system,which is proposed by the transition state tests such as the aero-engine high-altitude stage thrust transients.69The control system framework is shown in Fig.3669.The results of the experimental tests demonstrate that the intake environment simulation in the engine transition state test can be considerably improved in terms of dynamic reaction speed, control accuracy, and anti-disturbance capability by the deployment of ADRC technology based on the Linear Expansion State Observer (LESO).Similarly, a cascade ADRC is proposed to further improve the control quality.70Since the ADRC requires the differential signal of the system state, Zhang et al.studied the Levant differentiator and proposed a parameter tuning algorithm.71The effectiveness of the method was preliminary verified in the signal processing of AGTF.For the signal noise, Bai et al.proposed a tracking differentiator based measurement noise suppression and system phase compensator design method, which is expected to improve the pressure control accuracy of AGTF.72

Additionally,because the AGTF is a complicated pipe network system,a sizable number of regulating valves serve as its primary means of regulation.The development of AGTF makes it more challenging to control air flow in a broad range with high precision; as a result, co-regulating several valves simultaneously become a practical method, which necessitates the controller’s ability to coordinate the operation of each regulating valve.A two-valve cooperative technique based on open loop-closed loop composite control was presented by Liu et al.73, which may make use of the benefits of a largediameter butterfly valve for quick adjustment of big flows and a sleeve valve for precise adjustment of tiny flows.Similar to this, Liu et al.74have suggested a multi-valve cooperative control based on control allocation.By optimizing control allocation,this control can accomplish precise pressure control at AGTF,and the constructed controller has a certain level of resilience.

5.2.Multivariable control

Fig.36 Schematic diagram of intake pressure control system based on LADRC.69

The capacity of the control system to manage the temperature and pressure directly impacts the ability of the flight environment simulation test on AGTF, which is a system to replicate the inlet air conditions (total inlet air temperature and pressure) of an aero-engine.In fact, compared with the real flight environment of the aero-engine, the approximation degree of the simulated flight environment of the AGTF depends on the control accuracy of the intake temperature and pressure of the engine,as well as the control accuracy of the exhaust pressure.To enhance the flight environment simulation test capability of AGTF, research on the cooperative control of temperature and pressure of the flight environment simulation system is crucial.As a result, both domestic and international scholars have focused a lot of their attention on this control issue.Traditional single-variable control methods are no longer effective due to the coupling of system pressure and temperature dynamics.Hence this section gives an overview of multivariable control approaches for AGTF.

Bolk researched a multivariable control method based on target tracking for AGTF in order to realize the continuous simulation of engine airborne full mission profile flight trajectory.75He then designed the multivariable controller by LQ optimization method in order to realize the automatic switching of the controlled quantity among different working points.75Zhu et al.developed a PI gain scheduling controller design approach based on LMI pole placement.Based on the benefits of PI gain scheduling methodology and LMI pole placement method, the simulation verification of temperature and pressure cooperative control of the flight environment simulation is accomplished.76In order to achieve optimal control,Borairi et al.used the state space analysis method to design feedforward and feedback controller for the decoupling control of intake air temperature and flow rate of the AGTF in Ottawa, Canada.By analyzing the coupling characteristics between intake air temperature and flow rate, he was able to determine the coupling matrix between the two variables.33The performance of the AGTF control system is actually constrained by influencing factors like actuator uncertainty,2,77sensor noise,78temperature delay uncertainty,79large working envelope uncertainty,80and pipe network heat transfer uncertainty81in the flight environment simulation system, and it is necessary to deal with various influencing factors explicitly.For these robust control issues outlined above, Zhu et al.78have conducted a number of studies on control approaches integrated with μ-synthesis theory.They proposed a twodegree-of-freedom μ-synthesis control method based on the extended Kalman filter to solve the robust control problem of temperature and pressure sensors with noise in the flight environment simulation system.This method integrates the extended Kalman filter into the two-degree-of-freedom synthesis control framework (Fig.37) to realize the temperature–pressure co-simulation verification in the presence of sensor noise.78Zhu et al.79used multiplicative uncertainty to describe the inherent delay characteristics of temperature in the flight environment simulation system and considered it into the μsynthesis design framework for controller design,and they carried out the simulation of temperature and pressure control to address the robust control problem of large delay uncertainty in temperature due to long pipeline flow.It is validated that the flight environment simulation system’s temperature and pressure controls operate reliably in the situations of considerable temperature delay.79For strong coupling and large uncertainties, Liu et al.presented a reference model based μ-synthesis design for AGTF,which effectively improves the tracking performance and disturbance rejection performance.In addition,several variants of the μ-synthesis approach are comprehensively discussed.82,83

Fig.37 Schematic diagram of μ synthesis controller design.78

The study and development of high-performance gas turbine engines as well as Turbine-Based Combined Cycle(TBCC)engines have been sparked in recent years by the global demand for supersonic vehicles, and this progress has continued to expand the operational envelope of the vehicles.A broader working envelope will be supported by the flight environment simulation system, which will feed the engine with flight environment conditions.Therefore, the control system of FESS has a significant problem in establishing robust control across the whole operating envelope.Based on the benefits of Linear Parameter Variation(LPV)systems to handle large uncertainties,combined with the robust performance of μ-synthesis control in the local range,Zhu et al.proposed a μ-synthesis design method for two-degree-of-freedom integral LPVs to achieve robust simulation verification within the full envelope of the flight environment simulation system.80The flight environment simulation system is distinguished by a vast pipe network structure,and the heat transfer of this network will affect the flight environment simulation system’s ability to manage temperature and pressure,particularly during the process of quick temperature regulation.To enhance the dynamic control performance of temperature, the heat transfer of the pipe network should be considered in the controller design process.Its effect is a significant source of uncertainty for the flight environment simulation system.Zhu et al.81proposed an improved robust optimal model reference adaptive control method based on the linear system with matching uncertainty and perturbation to address this issue.They did this by introducing the matching uncertainty equation of the heat transfer effect of the pipe network into the state equation (Fig.3881).The technique confirms the robust control performance of the adaptive controller for the test process including Mach Dash and Zoom-Climb based on numerical simulation tests and further improves the control accuracy of the temperature and pressure of the flight environment simulation system.81Furthermore,Liu et al.83proposed a μ-synthesis-based robust L1adaptive control method for AGTF to achieve excellent control performance within a wide working envelope.The method avoids complex gain scheduling design.As shown in Fig.3983, the μ controller is used as a baseline controller to address coupling,while the L1adaptive compensation is used to cancel out the large(matched and unmatched) uncertainties.83

The traditional controller also has a tendency to cause the hydraulic actuator of the regulating valve to achieve a condition of position and rate saturation due to the sluggish dynamics of the actuator.Thus, Liu et al.developed an anti-windup design technique based on H2/H∞optimization, which significantly enhances the anti-windup performance of the closedloop system and minimizes performance deterioration of the control system in the presence of saturation.84

Fig.38 Constructive and schematic diagram of modified optimal control adaptive control system.81

Fig.39 Architecture of robust L1 adaptive control.83

Moreover,as a highly nonlinear system,the AGTF requires a controller with multi-source information sensing, adaptive and self-learning capabilities to ensure optimal operation during flight environment simulation.Additionally, a highprecision model can provide important unknown information to the control system.The intelligent decision-making system utilizes data from the whole AGTF system to achieve collaborative optimization and resource allocation among the subsystems of AGTF, improving efficiency and intelligence.The flight envelope of advanced aero-engines, such as TBCC engines, variable cycle engines, and hypersonic civil engines, has become wider,and operating conditions are complex and variable.The future AGTF faces challenges such as changes in piping characteristics, exhaust diffuser pneumatic characteristics, regulator throttling and clearance characteristics, which may constrain control quality improvement.Overcoming these challenges involves using observers or online models to estimate and eliminate numerous sources of disturbances before they affect the controlled system.This results in fast, robust,and highly accurate control that can perform multi-source disturbance suppression, which is an important trend in AGTF control.Control algorithms include sliding mode control,model predictive control, and neural network intelligent control.The future control of AGTF will require a variety of control objectives, different control methods, and control flexibility to meet the demand for adaptive, autonomous tuning, and autonomous decision-making.

5.3.Brief summary

Control is the foundation to improve high-quality flight environment simulation for the AGTF.This section summarizes the various control technologies used in the development process of AGTF, the summary of various control methods is shown in Table 5.From the perspective of its development,the early single-variable control technology has been difficult to meet the requirements of the new aero-engine test for the flight environment.At present, multivariable control has been engineered on several AGTFs.With the advancement of controller computing power and artificial intelligence technology,there is a growing interest in the application of intelligent con-trol algorithms to AGTF systems.However, in recent times,these intelligent control algorithms have shown limited effectiveness in actual engineering applications.

Table 5 Summary of various control methods.

6.Recommendations for future research

6.1.More advanced test methods and measurement technologies

With the continuous advancement of aviation propulsion systems in terms of efficiency,intelligence,and environmental sustainability, there arises a demand for AGTF systems to have improved and comprehensive testing capabilities.These capabilities encompass fulfilling stricter test index requirements,utilizing sophisticated measurement technology, and demonstrating adaptability to a broader array of assessment tasks, among other factors.This development trend will promote the development of test methods and measurement technologies of AGTF.On the other hand, with the development of technologies such as artificial intelligence,Internet of Things,massive data processing, virtual reality and high-precision numerical simulation,it is possible to update high-altitude simulation test technology of AGTF.The successful application of these advanced technologies will greatly enhance the authenticity of the aero-engine high-altitude flight environment simulation test, greatly improve the efficiency and safety of the test,and promote AGTF towards a more digital and intelligent development direction.In the near future,AGTF will have more powerful test capabilities flight for environment simulation,and will be able to simulate the flight environment of complex flight mission profiles with continuous changes.The future AGTF will be more intelligent and humanized,which will greatly reduce the burden of the test personnel and liberate the test equipment operators from the heavy and intense test operations.

6.2.Dynamic modeling with high accuracy

The quasi-one-dimensional flow model of AGTF has high accuracy and eliminates many limitations of lumped parameter model.However,this modeling method brings more adjustable coefficients, such as heat transfer coefficient, friction coefficient, local loss coefficient, etc.How to obtain these coefficients accurately is a big challenge.Until now, these coefficients have only been obtained through a large number of specialized tests.The AGTF has carried out a large number of high-altitude simulation tests, in which each equipment has accumulated large amount of test data.Although the data can be used to fit these coefficients,it is very difficult to select valuable data from so many test data to correct these coefficients.In the future, data processing methods based on machine learning and intelligent modeling methods based on massive test data will become the focus of research.

Simultaneously, the influence of air humidity was not considered in previous flight environment simulation tests.With the refinement of aero-engine flight environment simulation,the future humidity simulation will be gradually paid attention to.Meanwhile,the humidity was not considered in the modeling process of AGTF equipment,and the existing model could not simulate the influence of humidity on engine performance.In the future, with the continuous improvement of the model,the influence of humidity will be taken into account.

6.3.Multidisciplinary joint simulation

As a complex system, AGTF integrates the pneumatic, heat transfer,mechanical,hydraulic and electrical theories.The single simulation mode will limit the accuracy of the model.It is a feasible choice to build their own high-precision models according to the characteristics of each discipline,and then carry out multidisciplinary joint simulation.The development trend is to use a unified platform for scheduling individual models,which are usually built in different software.This requires addressing the interaction between the software.In addition, we need to pay attention to the balance between the complexity of the model and the calculation speed.Achieving the real-time requirement is the basic condition, which can verify the controller in the hardware in the loop.The ultimate goal is to meet the requirements of control system simulation and verification.

Moreover, as a system with high requirements for safety,the fault detection,diagnosis,health assessment,and monitoring of AGTF have gradually become important system functions.Especially, advanced aero-engines have increasingly high requirements for the test environment of AGTF.As a virtual mapping of real physical systems,digital twin system provides a solution to the above requirements.The multidisciplinary joint simulation will provide the foundation for the establishment of digital twin system.By improving the accuracy of the model,it is a feasible way to establish twins for specific purposes,such as equipment condition monitoring,system fault prediction, etc.

6.4.Advanced control

As a huge system, the AGTF is composed of thousands of equipment.During the high-altitude simulation test, a large amount of equipment cooperates with each other closely and works together efficiently.The control of AGTF is a typical process control.In the future development,the control of such large-scale complex system will adopt the mode of combining various control methods, and adopt different control methods at different system levels.In the actual operation level, each subsystem will adopt the traditional single-variable control or multivariable control method for process control, which is dependent on respective functional requirements and actual characteristics.Some traditional and mature control algorithms, such as sliding mode control,85model predictive control, robust control, etc., will be used at the actual operation level.In the top-level system, neural network intelligent control86and other advanced intelligent control algorithms will be used to realize cooperative scheduling and parallel operation among different subsystems, which can ensure efficient cooperation among subsystems.

7.Conclusions

This review article provides the necessary theoretical basis,clear development context and latest research progress of AGTF for control application.AGTF plays an important role in the performance testing of aero-engines.Current highprecision models and multiple simulation tools provide a more realistic and comprehensive evaluation of new control technologies.Moreover, multivariable control technology has shown significant advantages in command tracking and disturbance rejection.For more advanced intelligent control technology, the development of intelligent control systems with self-learning and autonomous decision-making capabilities has become crucial.In the future,high-altitude simulation test will be more intelligent and efficient, and the AGTF model combined with artificial intelligence will have higher accuracy.Furthermore,with the support of multidisciplinary joint simulation, AGTF is expected to develop digital twin systems,which will greatly improve the security and reliability for the AGTF.All these provide key technical support for AGTF to test the new-generation aero-engine.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This study was co-supported by the National Science and Technology Major Project, China (No.J2019-V-0010-0104)and Zhejiang Provincial Natural Science Foundation of China(No.LQ23E060007).